What do the following two equations represent? $-x+4y = 5$ $-2x+8y = -5$
Answer: Putting the first equation in $y = mx + b$ form gives: $-x+4y = 5$ $4y = x+5$ $y = \dfrac{1}{4}x + \dfrac{5}{4}$ Putting the second equation in $y = mx + b$ form gives: $-2x+8y = -5$ $8y = 2x-5$ $y = \dfrac{1}{4}x - \dfrac{5}{8}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.